Nonlinear Dynamics of Superflow in 3He-B: The Coupling of Sound and Helmholtz Oscillations

Abstract

The nonlinear relation between supercurrent and superfluid velocity:js(vs)=Ρsvs (1-(vs/vc)2/3)provides a coupling mechanism between the sound and Helmholtz modes of a short cylindrical cavity closed by a superleak at the centre of one end. Appropriate nonlinear equations have been formulated and solved numerically. The simulations reveal an interesting coupling of sound and Helmholtz oscillations at large amplitude. If the driving frequency of the sound is above the (large amplitude) resonance by twice the (large amplitude) Helmholtz frequency, only an initial Helmholtz drive is required to set up combined Helmholtz and sound oscillations, which can then be sustained by off-resonance sound drive alone. The combined motion, in which Helmholtz oscillations are amplified by sound drive, has been observed experimentally, but it decays when the Helmholtz drive is switched off, although it is sustained for a while by Helmholtz drive alone. Modified simulations that allow for quasiparticle relaxation show that slow relaxation is the probable reason that the combined motion decays without Helmholtz drive even at the lowest temperatures where the resonance Q is high. Comparison of simulations and experiment also gives evidence for larger dissipation at large amplitudes and associated memory effects. The simulations show that in the combined motion the negative slope region of js(vs) for vs>vc is being explored.